President Obama discusses the mission against Osama bin Laden on May 1, 2011, with national security adviser Tom Donilon. / Getty Images

by Aamer Madhani, USA TODAY

by Aamer Madhani, USA TODAY

If National Security adviser Tom Donilon wants to be the next secretary of State, he's not saying.

After delivering a speech previewing President Obama's upcoming trip to east Asia and detailing the administration's "Asia pivot" on Thursday, Donilon was asked during a short question-and-answer session about his interest in the job.

Donilon, who delivered his remarks at the Washington Center for Strategic and International Studies, answered in detail another part of the questioner's query on the timing of Obama's trip to Burma. When pressed on his interest in the State job, Donilon only smiled and moved on the next question.

Hillary Rodham Clinton has said she would like to leave the post early in Obama's second term.

The president said at his news conference Wednesday that he's made no decision on whom he'll pick for the spot, though he vigorously defended another contender for the job, United Nations Ambassador Susan Rice, who has faced sharp criticism from Republicans for incorrectly stating that an attack on the U.S. Consulate in Benghazi, Libya, was precipitated by a protest.

Donilon may also be in the mix to serve as Obama's next chief of staff should Jack Lew become the next Treasury secretary. Like Clinton, Treasury Secretary Timothy Geithner has said he would like to leave his post before Obama's inauguration in January.